Charcloth and I have been discussing this issue in a PM, and I'll reiterate some of that here. I just got a Saga SS10 and am messing with it to try and arrive at the sound I want.

I put a fibreskin head on which dulled it down somewhat, but I'm still not quite getting that tubby sound that is desired. After listening carefully, I didn't like the sort of "tinny" hollow sounding overtones I was getting. I experimented with rags, which are hard to control, and have ended up with a 2" X 2" piece of soft sponge. It seems to effectively mute the tinniness. Also I can easily stuff the sponge behind the coordinator rod and slide it from one end to the other, which gives some slight variation in the tubbiness effect - especially when it's directly under the bridge.

Of course the side effect is to cut down on volume, and since I normally play a resonator banjo, this is causing quite a bit of character development. Hell, maybe next I'll get a huge honking amp and go electric !!